The traditional approach to measure the currents of power conductors is to install a current sensor such as a current transformer or a clamp-on Hall-effect sensor to each conductor. This approach has been practiced by electrical industry for years. While it can provide accurate measurement of the conductor current, the approach has a major limitation: the sensor must be clamped-on to each conductor for measurement. If the conductors cannot be separated or cannot be accessed individually, it is not possible to measure the conductor current using such techniques. Since cases involving bundled conductors are not uncommon, industry has a strong need for techniques that can measure currents in a group of difficult-to-separate conductors. A classical example of such a need is to measure the currents in conductors that are enclosed in an electrical conduit. Another example is to measure the currents in a multi-conductor cable such as the Romex cable. A third example involves the measurement of currents in overhead power lines without using expensive, high voltage, clamp-on current transformers.
In recent years, a new current measurement technique that has the potential to overcome the above shortcoming has emerged. The technique involves the use of an array of magnetic field sensing elements placed in close proximity to the conductors of interest. The idea is to calculate the conductor currents based on the magnetic fields measured by the sensing elements. J. T. Scoville and P. I. Peterson, for example, presented an idea of using arrays of magnetic field sensors for the purposes of current sensing and of rejecting background magnetic field noises (“A low-cost multiple hall probe current transducer” Review of Scientific Instrumentation Vol 62, no. 3, pp. 755-760, 1991). In their article (“Precise DC current sensors” IEEE Instrumentation and Measurement Technology Conference pp. 1479-1483, 1996), P. Ripka, P. Kejic, P. Kaspar, and K. Draxler also proposed the sensor array method for DC current measurement but different magnetic field sensors were used. The article by G. D'Antona, L. D. Rienzo, R. Ottoboni, and A. Manara, (“Processing Magnetic Sensor Array Data for AC Current Measurement in Multiconductor Systems,” IEEE Transactions On Instrumentation And Measurement. Vol 50, no. 5, pp. 1289-1295, 2001.) proposed to use the finite element method to determining the relationship between the conductor currents and sensed magnetic fields so that more accurate current can be measured. The patented ideas in the area of sensor array based current measurement method include U.S. Pat. Nos. 5,438,256 and 5,473,244. U.S. Pat. No. 5,438,256 disclosed a method to measure currents in overhead power lines using magnetic field sensor array deployed at the ground level. U.S. Pat. No. 5,473,244 proposed a method to determine the currents in the conductors of Romex cables which are commonly used in homes.
All of the above techniques need to solve a common problem before they can be applied for current measurement. They need to establish the relationship between the currents to be determined and the magnetic fields measured. This relationship is a function of the geometric locations of the conductors and sensors, i.e. the layout of conductors and sensors. If such geometric information is available, the relationship can be established. For example, U.S. Pat. No. 5,438,256 and the technical articles cited earlier use the known geometric parameters of the conductors and sensors to establish the relationship and thereby to calculate the conductor currents using the established relationships and the sensed quantities. Unfortunately, for cases where the geometric parameters are unknown, such as the Romex cable case, it has become very difficult to measure the current using the sensor array technique since the relationship cannot be established. U.S. Pat. No. 5,473,244 proposed one idea to solve the problem. It involves the use of redundant sensors and an optimization algorithm. The algorithm is to figure out a set of current values such that the errors between the calculated magnetic fields and sensed magnetic fields are minimized. While this technique is theoretically sound, there is no guarantee to get the correct results since there are multiple local minimal solutions for the optimization problem.